Measuring & Predicting Stock Volatility

I have not of late, if I have ever, been making many contributions of value. Here is something I dreamt up while listening to Dave Allman's interview of Connie Brown. The purpose is to find stocks which will move in either direction, but do so rapidly.

My firsts filters were performed on NYSE stocks on June 2, 2003. Only stocks on June 2 with a close above 2.0 and a moving average of volume above 100,000 were accepted.

The formula for measuring volatility is this:

[ ATR(20) / MA(C,20) ] * [ HHV(H,20) / LLV(L,20) ] = "RBVol"

The greater the value, the greater the volatility.
In english, you take a twenty period Average True Range and divide by a simple moving average of the close. You then mulitiply that value by the highest high over the twenty bars divided by the lowest low over twenty bars.

Testing went as follows:

Group 1: Filter performed on aforementioned universe where only stocks with an RBVol greater than 0.1 and less than 10 were accepted. 37 stocks met the criteria.

Group 2-5: Groups of 24 randomly selected from aforementioned universe.

Calculated for each stock was the absolute percentage change between June 2, 2003 and twenty bars into the future (roughly July 2, 2003).

Group 1 has an average absolute percentage change of 15.9% with 8 stocks changing less than 5.5% (22%). Groups 2-5 have average absolute percentage changes of 5.9, 5.4, 3.7, & 7.0 (avg.: 5.5).

I just started working with this, so more testing is needed. There are some anomolies which may have to do with the quality of my data. (One stock looks to have undergone an unadjusted split) Also, there are a few stocks with closing prices below $5 which underwent a decline in price. Since there are trading restrictions on shorting such issues they should probably not be included.

I have never known the entire method of calculating beta. I have seen some of the math but because of my limited mathematical expertise was unable to understand the formula. Also, I was under the impression that beta was calculated in relation to an index - or the market in general - in which case this method would differ in that it is "stand-alone," so to speak.

I would be interested to see an explaination of beta if someone at Elite were willing to provide it.

My intention is to use this as one would likely use beta. My software does not come pre-programmed with a beta formula. And, were I to have such a formula I would still be wary to use it unless I understood the calcs myself.

You are right. I just read an article on CBSMarketwatch about low volatility stocks with good yields.

Beta is described as "a measure of a stock's volatility relative to the market based on historical trading patterns. For example, a stock with a beta of 0.5 (the market beta is 1.0) will be expected to move half as much as the market. "

And then I am also thinking, wouldn't a screen of stocks for a certain average daily range over the previous N days be enough?

What is the rationale behind the second leg of your formula?
[ HHV(H,20) / LLV(L,20) ]

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For the foreseable future I will not be daytrading. As a result, I am interested in issues which, for example, range between $5 and $20 in price over a month moreso than issues ranging between $20 and $22 over a similar period.

Conceptually speaking the first part of the equation measures day-to-day volatility of a stock relative to its price. The second half measures the follow-through or trending behaviour or overall range of the issue.

Were the second half not present I would expect to see some stocks which move very rapidly within a very narrow range. And, being that I am looking to hold positions for up to a week or three these would be of little use.

I take the average range (just high - low) over X days (I've used 20 days) and divide that by the stock price. Then I cutoff at a certain percentage till I get a good list of stocks to work with.

This way if I have two stocks, each with a $2 range for example, but one costs $20 and the other costs $60, I easily see I may get more "bang for my buck" with the $20 stock (it'll rank higher). Of course, the 'bang' can work against you so position sizing is still paramount.

Be careful with penny stocks, though. I was cutting off at $5 per share and that may have been a bit low.

Is this question posed to the users of beta or my formula?
If you mean there is a simpler approach than what I have put forth then I'd be curious to see more precisely what you mean.

Also, with beta am I correct in believing that values 1.0- (less movement than the general market, eg: utility stocks), 1.0+ (more movement), and likewise when negative except counter-market movement?

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That's exactly the idea. Theoretically, the beta is the multiplicative coefficient found in the linear regression of the stock returns on the market (index) returns. The formula is the covariance of the two return histories divided by the variance of the market returns.